The equation of radiative transfer for a plane-parallel medium is solved by assuming that second-order scattering and above is negligible. Radiation involved in the first scattering process is taken into account. The solution is used to determine the output of a receiver having a narrow field of view and an arbitrary response function. A scattering factor k¯ is defined for convenient determination of the approximate influence of the scattered radiation on reception through aerosols such as rain, fog, and mist. The factor k¯ can be used to define the conditions under which one should employ multiple scattering as opposed to single scattering theory. In order to utilize the results one must know the normalized Mie intensity function, albedo, and optical depth of the aerosol.
D. E. Setzer, "Influence of Scattered Radiation on Narrow Field of View Communication Links," Appl. Opt. 10, 109-113 (1971)